# IBM Researcher Reveals Details on Quantum Entanglement Forging

## IBM Quantum has introduced entanglement forging, a technique to double the size of systems that can be simulated using quantum hardware. We spoke to one of the researchers who led the development of this method.

In recent years, physicists and engineers worldwide have been exploring the potential of quantum technologies—systems based on the principles of quantum mechanics and quantum physics. These technologies, which include computers, sensors, cryptographic approaches, simulation platforms, metrology tools, and imaging devices, have the potential to significantly outperform conventional technologies, both in terms of speed and efficiency.

IBM Quantum recently devised a promising method that could allow engineers to carry out larger calculations and simulations using quantum hardware.

To learn more about this method, dubbed “entanglement forging,” we interviewed Sarah Sheldon, a senior manager at IBM Quantum’s Almaden Research Center in San Jose, who was closely involved in its development.

*Sarah Sheldon, senior manager of quantum theory and applications at IBM Quantum. Image used courtesy of IBM Quantum*

**Before we begin, can you briefly introduce yourself and your academic and professional path? What got you interested in quantum physics and quantum computing at IBM?**

**Sara Sheldon:** I studied quantum control in magnetic resonance systems for my Ph.D., which allowed me to think about how to improve quantum gates when I joined IBM eight years ago as a postdoc. Since I started here, I've also worked on developing techniques for characterizing quantum devices and extending the capabilities of our current quantum systems as a research staff member and a manager.

I was drawn to IBM immediately after grad school because of its world-class team and the ability to work collaboratively toward big goals. It's been exciting to see our team in the field of quantum computing as a whole grow tremendously and to realize the amazing systems and capabilities that we have today.

**You recently published an interesting paper in PRX Quantum. Could you tell us what it was about and what its main achievements were?**

**Sheldon:** In this paper we introduce a new method, which we call entanglement forging, to double the size of a system we can simulate on quantum hardware. Entanglement forging allows us to partition quantum systems into two easier-to-simulate halves by pushing some of the computation onto the classical computer where the two halves of the problem are in classical post-processing. By reducing the problem size, we increase the accuracy of our results. We demonstrate this method by using five qubits to simulate the ground state of a water molecule under different geometries.

**How does classical entanglement forging help smaller quantum circuits perform more complex calculations? In what ways does it differ from previously-proposed approaches? **

**Sheldon:** Entanglement forging divides the system being simulated in two, so that we can use half the number of qubits in each individual experiment. By breaking down the problem into smaller pieces, we end up with circuits that use both fewer qubits and fewer gates. Consequently, the smaller circuits give more accurate results. In order to calculate expectation values on the full system, we have to combine the outcomes of the smaller circuits from each half in a weighted sum on a classical computer.

*Classically forged entanglement. Image used courtesy of PRX Quantum*

We use a standard algebraic decomposition (singular value decomposition) to decompose the state of the system into two. The number of terms in this decomposition depends on how strongly the two halves are entangled, so we restrict the scope to problems with weak entanglements, such as the molecular system discussed in the paper. How hard a problem one can address with entanglement forging will depend on the classical and quantum resources available.

**Considering All About Circuits’ target audience of electrical engineers, could you tell us about any circuit design that went into your research? Or perhaps the implications of your research on future circuit design within the computing space? **

**Sheldon:** In quantum, we often use the “circuits” to refer to both the physical circuit that makes up our quantum device and the sequence of operations applied to implement the algorithm. When we describe improving the accuracy of our quantum circuit with entanglement forging, we mean the algorithmic implementation.

*Example of a quantum circuit, including a quantum teleportation algorithm. Image used courtesy of Qiskit*

When it comes to physical circuits, IBM Quantum devices consist of superconducting circuits that operate at low temperatures and are controlled by microwave signals. This work leveraged a 27-qubit device developed and deployed by IBM Quantum through our cloud service.

**In your study, you demonstrated the effectiveness of your method by using it to model the H2O molecule. Can you share any performance metrics from the demonstration?**

**Sheldon:** In the paper, we look at the ground state energy of the water molecule under different geometries: at equilibrium, under symmetric stretching of the two hydrogen atoms, pulling one hydrogen atom off, and rotating the bond angle.

For entanglement forging to scale efficiently, we require that the two halves of the system that are run on the quantum computer separately are weakly entangled. This assumption is most valid for the equilibrium geometry, where we measure the ground state energy to be within 10 millihartree of the exact value. In the simulation, we believe that it is possible—with entanglement forging—to reach within 1.6 mHa of the exact energy, equivalent to the value required for chemical accuracy.

**What do you feel are the most important implications of your study? Could you provide some examples of how you think classical entanglement forging could be effectively applied in the future?**

**Sheldon:** Entanglement forging is a method that allows us to move some of the computation from the quantum computer to a classical computer. This yields more accurate results than we could otherwise achieve on noisy quantum devices. In the paper, we demonstrate this using five qubits to simulate the water molecule. But if we could obtain accurate results on a larger number of qubits, we could imagine simulating problems up to twice the size of the quantum device.

The scaling of the problem depends on how much entanglement has to be reconstructed on the classical computer. In this work, we highlight systems that have two weekly entangled halves, like the spin-up and spin-down orbitals of certain molecules, that would be particularly amenable to forging. We think simulations of physical systems partitioned into two parts of a lattice would be another candidate for this approach. Finding other problems that could benefit from entanglement forging with reasonable scaling is an interesting area of future research.

**What about your research might interest electrical engineers, even those who don’t work with quantum computing systems? **

**Sheldon:** There are many engineering challenges that we face in realizing useful quantum computers. This applies to all of the work that we do and not just entanglement forging. As mentioned already, our devices are made of superconducting circuits, and understanding the sources of noise in these devices and how to scale them up remain our primary experimental goals. We also control the state of the qubits on our devices with finely-calibrated microwave pulses. At IBM we build our own control electronics to meet the specific demands of controlling quantum hardware.

**What will be the next steps in your research? **

**Sheldon:** There are questions we would like to explore further like what other problems can we apply entanglement forging to or what kind of knowledge of the system do we need to set up a simulation with forging. More generally though, entanglement forging belongs to a larger set of methods that employ classical resources to increase the size or the accuracy of a problem that can be solved with quantum computing. Error mitigation is another tool that does this. We plan to explore the trade space between classical and quantum computation to keep expanding the size and complexity of problems that we can study.

The new quantum computing method developed at IBM Quantum was introduced in a paper published in PRX Quantum. In the future, this research could help improve the scalability of quantum simulators, making them easier to apply to more complex real-world problems.

To find out more about this recent research and the systems that Sheldon and her colleagues are developing, visit IBM Quantum's homepage.

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